On the l1 procrustes problem

Authors:
Nickolay T. Trendafilov
Affiliations:
Faculty of Computing, Engineering and Mathematical Sciences, University of the West of England, Bristol BS16 1QY, UK
Venue:
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Year:
2003

Citing 6
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Abstract

In this paper, the well-known Procrustes problem is reconsidered. The usual least squares objective function is replaced by more robust one, based on a smooth approximation of the ℓ1 matrix norm. This smooth approximation to the ℓ1 Procrustes problem is solved making use of the projected gradient method. The Procrustes problem with partially specified target is treated and solved as well. Several classical numerical examples from factor analysis (well-known with their least squares Procrustes solutions) are solved with respect to the smooth approximation of the ℓ1 matrix norm goodness-of-fit measure.